The noncollinear interlayer coupling in NiFe/NiO/NiFe trilayers

The interlayer coupling and magnetization reversal behaviors in NiFe/NiO/NiFe trilayers were investigated using polarized neutron reflectivity and Monte Carlo (MC) simulations. Our results reveal that the shape of NiFe loops transitions from square to tilted as the NiO thicknesses decrease, indicating changes in the direction of NiFe layer’s easy axis. This phenomenon can be attributed to variations occurring at NiO/NiFe interfaces for different NiO layer thicknesses. With thin NiO layer, interdiffusion at the NiO/NiFe interfaces leads to frustrated coupling, resulting in a noncollinear interlayer coupling. This observation is supported by MC simulations. Conversely, hardly any coupling frustration is observed for the sample with a thick NiO layer. Our findings propose a novel way to tailor the interlayer coupling through interface engineering.


Introduction
The interlayer exchange coupling (IEC) in magnetic multilayers has attracted considerable attention since the discovery of giant magnetoresistance effect in ferromagnet (FM)/spacer/FM systems [1], which sparked the development Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
of spintronics [2].The spacer could be nonmagnetic or antiferromagnetic.The latter suggests that the antiferromagnetic spin structure can play a crucial role in modifying interlayer coupling [3].Moreover, antiferromagnets (AFMs) have emerged as key materials in spintronic devices due to their unique features compared to FMs [4][5][6].The propagation of spin currents through AFMs has a significant impact on spin transport properties and provides opportunities for the manipulation of spin-orbital torque (SOT) [7][8][9][10][11].For example, the skyrmions have been observed in perpendicularly magnetized multilayers with the AFM spacers, exhibiting nonmagnetic or antiferromagnetic IEC [12].Therefore, investigating the role of AFMs in IEC of magnetic films is of great importance to advance the field of AFM spintronics.Different types of AFM metal have been used as spacers, resulting in the observation of 90 • IEC between FM layers [13][14][15][16].This phenomenon can be well explained within the proximity model, which assumes significant thickness fluctuation in the AFM spacer [17].Zhan et al proposed that the noncollinear interlayer coupling between the FM/AFM interfaces could compete with the AFM anisotropy and lead to the transfer of the exchange bias (EB) effect in NiFe1/FeMn/NiFe2 multilayers [16].Furthermore, noncollinear coupling can also be observed in systems with an AFM insulator (AFMI), such as Fe 3 O 4 /NiO/Fe 3 O 4 [18], NiFe/NiO/Co [19], Fe/NiO/Fe [20], Co/NiO/Fe [21].Brambilla et al argued that the proximity model cannot reproduce the magnetization behaviors in FM/AFMI/FM system, where a significant contribution of interface direct exchange couplings is expected [20].Due to the difficulty in directly characterizing the AFM spin structures, there are still controversies in understanding the mechanism of noncollinear IEC across AFMI layer [18,19,21].Additionally, while interface mixing is commonly observed in FM/AFMI heterostructures [22][23][24][25][26][27], which can modify the nearest-neighbor exchange across the interface [28,29], its impacts on the IEC are seldom reported.Although the origin and modifications of the noncollinear IEC is still under intense research, its applications in sensors and spintronic devices deserve attention.Liu et al reported that the perpendicular arrangement of FM spins could be used to produce excellent magnetoresistive field sensors with linear and reversal responses [30].Nagashima et al [31] and Zhong et al [32] found that the noncollinear IEC could lead to a new type of magnetic material called quasi-AFM, with alternating antiparallel magnetic domains whose size can be easily controlled by IEC.Quasi-AFM materials exhibit both AFM and FM properties [31], which may be beneficial for advances in AFM spintronics.Therefore, further investigations are required to unveil the underlying mechanism of the noncollinear interlayer coupling in FM/AFMI/FM systems from both physical and technological perspectives.
In this study, we employed polarized neutron reflection (PNR), x-ray reflection (XRR) and Monte Carlo (MC) simulations to investigate the role of AFM/FM interfaces in noncollinear IEC.We confirmed that the diffusion-induced exchange coupling frustration is the key factor contributing to noncollinear interlayer coupling in our NiFe/NiO/NiFe samples.Our findings suggest a novel approach to modifying the interlayer coupling in magnetic multilayers.

Experiments
The samples were fabricated on a silicon wafer in a magneto sputtering chamber with a base pressure better than 5 × 10 −6 Pa.The sample structures were Ta(4)/NiFe(10)/NiO(t)/NiFe(4)/FeMn(8)/Ta(4), with numbers in blankets symbolizing the thickness of each layer in nanometer.The NiO layer thickness, denoted as t, was varied between 1.4 nm and 3 nm to control the interlayer coupling between the two NiFe layers as shown in figure S1 of the supplementary material.A 4 nm thick Ta served as a buffer layer to promote (111) texture in the multilayers, and a capping Ta layer was deposited to protect the sample from oxidization.The 10 nm thick NiFe layer was referred to as the free-NiFe layer, while the 4 nm thick NiFe layer biased by the FeMn layer was referred to as the pinned-NiFe layer.All samples were deposited under an external field of 280 Oe, and were then annealed at 200 • C for 2 h under a magnetic field.Both external fields were applied in the same in-plane direction.
The hysteresis loops were recorded using a vibrating sample magnetometer, as shown in figure 1.The switching field was applied along the direction of the annealing field.For the sample with a NiO thickness of 1.5 nm (referred to as NiO15), the free-NiFe layer shows a negligible loop offset (∼0.8 Oe), while the pinned-NiFe layer displays a pronounced loop shift.Furthermore, the tilted loops suggest the easy axis switches to a direction perpendicular to the external field, indicating a noncollinear coupling between the two NiFe layers, as expected based on previous studies [15,16,30].Notably, the pinned NiFe in the NiO15 sample shows a more pronounced tilting in the loop compared to the free NiFe, which can be attributed to different interface structures, as discussed below.As the NiO layer thickness increases to 3 nm (referred to as NiO30), the free-NiFe layer continues to exhibit a negligible loop offset (∼0.8 Oe), while the pinned-NiFe layer maintains a significant loop offset (∼376 Oe).The negligible loop offsets in the free-NiFe layers are consistent with a previous experiment [33].Note that the pinned-NiFe layer in the NiO30 sample shows a relatively increased loop shift compared to that in the NiO15 sample.This is possibly due to an increase NiO thickness underneath the NiFe/FeMn heterostructure, which could enhance the EB effect [34,35].Interestingly, the hysteresis loops for both NiFe layers in the NiO30 sample became much squarer in shapes, revealing an easy axis along the applied field direction and a significant reduction in the strength of the noncollinear IEC.
To analyze the thin film structures, XRR measurements were conducted on the samples using a Rigaku Smartlab xray diffractometer.The reflectivity was recorded as a function of momentum transfer Q = 4πsinθ/λ, where θ and λ denote the angle and wavelength of incident beams.The reflectivity curves were further fitted using a layer model with the GenX package [36].To assess the goodness of fit, we employed the figure of merit (FOM), calculated as , where Y i and S i denote the ith experimental data and the corresponding model simulation value [36].Figure 2 shows the XRR data and corresponding fitting results for the NiO15 sample.We observed that a fitting model with sharp NiO/NiFe interfaces cannot accurately reproduce the experimental data with a FOM of 0.063, particularly for Q larger than 0.2 Å −1 .Therefore, we introduced two interfacial layers, denoted as X_bot and X_top, at the NiO/NiFe interfaces as shown in figure 2(b).By incorporating these interfacial layers, we achieved a satisfactory agreement between the experimental data and the simulation with a smaller FOM of 0.040, indicating the presence of interface layers at NiO/NiFe interfaces in the NiO15 sample.The thickness of the X_bot and X_top layers are found to be 0.7 nm and 1.3 nm respectively, agreeing well with previous reports [22,33].In contrast, the XRR results for the NiO30 sample revealed clean NiO/NiFe interfaces as shown in figure S2.The inclusion of interfacial layers resulted in poorer fitting for the NiO30 sample, suggesting rather different interface structures compared to the NiO15 sample.
To gain further insight into the nuclear and magnetic structures at the interfaces, PNR measurements were performed under an external field of 0.3 T at multi-purpose reflectometer of China Spallation Neutron Source [37].PNR serves as a powerful tool for characterizing magnetic moments within thin films and delving into buried interface structures.When neutrons are polarized parallel (or anti-parallel) to the applied magnetic field, those reflected from the sample while retaining the same polarization are recorded as Ruu (or Rdd).The spin asymmetry (SA), calculated as the difference between Ruu and Rdd reflectivity curves (i.e.SA = (Ruu − Rdd)/(Ruu + Rdd)), proves highly sensitive to the magnetism within thin films.Precise fitting of PNR data yields essential film structure information, including the nuclear scattering length density (SLDn) and the magnetic profiles (SLDm) along the out-of-plane direction.Figure 3 displays the PNR experimental data and the fitting results for the NiO15 sample.Similar to the XRR fitting, we included two interfacial layers at the NiO/NiFe interfaces to achieve a satisfactory fit to the PNR data.To understand the influence of the two interface layers, we also showed the fitting model without any interfacial layers (the dotted line in figure 3(c)).The reflectivity curves and SA for both fitting models can be found in figures 3(a) and (b).It can be observed that the SA of the model lacking interfacial layers falls short in reproducing the experimental data at Q-values around 0.05 Å −1 , 0.085 Å −1 , and above 0.095 Å −1 .Consequently, it is evident that the model with interface layers better reproduces the experimental data compared to the model without interfacial layers.It is noteworthy that both NiFe layers exhibit a saturated magnetization of approximately 1.05 µ B /f.u., which is close to its bulk value.However, the NiO layer shows nearly zero magnetization, indicating the possibility of an antiferromagnetic or a paramagnetic order.Firstly, the thin NiO films have been exhibited a Néel temperature that can exceed their bulk value due to the proximity to ferromagnetic materials [3,12,29,38].Secondly, the interlayer coupling across AFMI spacer is expected to decrease when the AFM order turns to disappear [29].Although our NiO15 sample exhibits a significant noncollinear interlayer coupling, the possibility of a paramagnetic order within the NiO spacer cannot be entirely ruled out.To simplify the following simulations, we consider the NiO spacer with an AFM order.
It is worth noting that both interface layers exhibit magnetism, albeit to different extents.Specifically, the X_bot layer displays a SLDm of 2.2 × 10 −6 Å −2 , whereas the SLDm of the X_top layer is 1.1 × 10 −6 Å −2 .This distinction suggests varying interface structures at both FM/AFM interfaces.Interface layers are commonly observed at the interface of NiO adjacent to FM materials such as NiFe [22][23][24], CoFe [25] and Fe [26,27].Additionally, the deposition sequence of the FM and AFM layers can also significantly influence the interfacial characteristics [39].Previous studies have indicated that a ferrimagnetic layer (e.g.Ni x Fe y O z [33] or Fe 3 O 4 [39]) could form at the bottom NiFe/NiO interface.In contrast, at the upper NiO/NiFe interface, Yu et al reported the formation of ferrites comprising FeO and Fe 2 O 3 , which are characterized by lower Curie temperatures and reduced magnetic moments [22].Consequently, it is reasonable in our PNR fitting that the X_bot layer at the lower NiFe/NiO interface exhibits stronger magnetism compared to the X_top layer at the upper NiO/NiFe interface.The interfacial mixing can influence the effective coupling between FM and AFM spins accordingly [28,29] and result in a frustrated interface coupling, which can induce noncollinear IEC as illustrated below.
We also conducted PNR measurements for the NiO30 sample under the same external field as shown in figure 4. While the SA calculated using the model with interfacial layers (i.e. the X_bot and X_top layers) adequately reproduces the experimental data for Q below 0.09 Å −1 , it notably deviates when Q exceeds this value.In contrast, a good agreement is observed in the whole Q range between the experimental results and the fitting curves generated by a model lacking interfacial layers, indicating significant interface structure changes in the NiO30 sample.Same as the NiO15 sample, the NiFe layers in NiO30 sample exhibit a strong FM order with a saturated magnetic moment of ∼1.05 µ B /f.u., while the NiO layer still shows almost negligible magnetization.However, differences can be observed at the NiFe/NiO interfaces for the NiO30 sample.Sharp interfaces are found at both NiFe/NiO interfaces, which can be attributed to improved crystalline texture and interface quality with an increase in the volume of AFM grains [40], thereby preventing the interface mixing.Therefore, the main difference in film structures of the NiO15 and NiO30 samples is primarily governed by the interdiffusion at NiO/NiFe interfaces.This interdiffusion, as discussed below, may be a key factor contributing to the changes in hysteresis loops with increasing NiO thickness.

Discussion
The above XRR and PNR data reveals the evolutions of interface layers at the NiO/NiFe interfaces.As the NiO thickness decreases, more significant interdiffusions are observed at the interfaces.Laureti et al [25,28] reported that the interdiffusion-induced chemical inhomogeneties can modulate the strength of the exchange coupling.Baruth et al [29] proposed that different terminations of NiO at the interface can change the interface coupling from FM coupling to AFM coupling.An intense interface mixing could lead to a frustrated interface coupling at FM/AFM interface.Based on the XRR and PNR results, we assume a more frustrated interface coupling can be found at the top NiO/NiFe interface compared to the bottom NiFe/NiO interface for the NiO15 sample.However, in the NiO30 sample little exchange coupling frustration can be observed at both AFM/FM interfaces.Consequently, we performed MC simulations on FM1/AFM1/FM2/AFM2 structure with interface coupling frustrations and investigated its relation with interlayer coupling.
FM1 denotes the free FM layer, while the FM2 is the pinned FM layer.The nearest-neighbor exchange coupling constant J FM2 for the FM2 layer was defined as the unit of energy and other parameters can be set accordingly [41] as shown in the supplementary material.Thus, the external field is defined as a reduced field, i.e. b = B/J FM2 which is commonly used in micromagnetic simulations [42].The exchange coupling constants for both FM/AFM1 interfaces are initially defined as J INT = −J FM2 /2, representing AFM interface coupling (AFIC).To introduce interface coupling frustrations at both FM1/AFM1 and AFM1/FM2 interfaces, a portion of the AFICs is randomly replaced by FM coupling of the same magnitude with concentrations of P int1 and P int2 , respectively.When P int1 = 1 (or P int2 = 1), the original AFIC become FM interface coupling (FIC).Based on the above results, we assume a moderate interface coupling frustration at the FM1/AFM1 with P int1 = 0.1, while the frustration concentration P int2 at the AFM1/FM2 interface varies from 0 to 1.This allows us to investigate the impact of the interface coupling frustrations on the interlayer coupling.Detailed information on the MC simulations can be found in the supplementary materials.
As depicted in figure 5(b), the free FM1 layer remains titled and almost unchanged with variation in P int2 due to the constant P int1 = 0.1 at the FM1/AFM1 interface.Square loops can be observed for FM2 layer when considering AFIC (P int2 = 0) and FIC (P int2 = 1) at AFM1/FM2 interface.However, for the frustrated interface coupling (P int2 = 0.5), FM2 layer exhibits tilted hysteresis loops suggesting an easy axis perpendicular to x-axis, indicating a noncollinear IEC consistent with the experimental findings.The effective noncollinear coupling strength is defined by the saturation field b eff of FM layers and its dependence on P int2 is illustrated in figure 5(c).As the bond dilution concentration steps up, b eff steadily increases in the FM2 layer, peaking at P int2 = 0.5 where randomly distributed FM and AFM bonds are introduced at the AFM1/FM2 interface.Therefore, the interface coupling frustrations at FM/AFM interface can induce a 90 • rotation in the easy axis of FM layer.Figure S3 further demonstrated that the frustrated FM/AFIC could lead to a strong effective field along y-axis, which aligns the FM spins perpendicular to the easy axis and results in noncollinear IEC.
Various mechanisms have been proposed to explain the noncollinear IEC across the AFMI layer.van der Heijden et al [18] and Camarero et al [19] proposed that the existence of spiraling spin structures exist in the AFMI spacer, which occur due to interfacial roughness and lead to noncollinear coupling between FM layers.On the other hand, other research [21] demonstrated that the different types of interface coupling at each FM/AFMI interface should be the primary reason for the occurrence of noncollinear coupling.By combining our experimental and simulation findings, we propose that the interface coupling frustration plays a crucial role in the evolution of interlayer coupling across the AFMI layer in our NiFe/NiO/NiFe samples.In the case of the NiO15 sample, intense interdiffusion at NiO/NiFe interfaces, particularly at the upper NiO/NiFe interface, results in frustrated interface coupling between FM and AFM layers, leading to tilting loops for both NiFe layers.However, with an increase in NiO thickness, the FM/AFM interface structures for the NiO30 sample improve, with almost no exchange coupling frustration, resulting in square loops for both NiFe layers.

Conclusion
In conclusion, we investigated the noncollinear interlayer coupling and its origin in NiFe/NiO/NiFe trilayers using PNR, XRR and MC simulations.Our study demonstrates that changes in the loop shape of the NiFe layers, as the NiO layer thickness increases, can be attributed to modifications occurring at the NiO/NiFe interfaces.Specifically, for the sample with a 15 Å thick NiO layer, interdiffusion takes place at both NiO/NiFe interfaces, leading to frustrated coupling and resulting in titled loops for NiFe layers.Conversely, for the thicker NiO sample, the FM/AFM interface structures improve, leading to minimal exchange coupling frustration and thus the acquisition of square loops.Our findings unveil the critical role of interface coupling frustration in inducing interlayer coupling through an insulating AFM layer.Furthermore, we propose a method to manipulate the interlayer coupling by designing appropriate interface structures.

Figure 1 .
Figure 1.Hysteresis loops for the NiO15 sample (a) and the NiO30 sample (b) with applied field along the deposition field direction.The vertical dotted line denotes the point where the external field reaches zero, while the horizontal dotted lines serve as visual guides to help distinguish between the two NiFe layers.The sketch illustrates the sample structures.

Figure 2 .
Figure 2. (a) X-ray reflectivity and (b) scattering length density profile for the NiO15 sample fitted by models with interfacial layers (red lines, FOM = 0.040) and without interfacial layers (blue line, FOM = 0.063).

Figure 3 .
Figure 3. (a) PNR data and (b) spin-asymmetry ratio for the NiO15 sample fitted by models with interfacial layers (solid lines, FOM = 0.018) and without interfacial layers (dotted line, FOM = 0.020).(c) Nuclear SLDn and magnetic SLDm with interfacial layers (solid lines) and without interfacial layers (dotted line).

Figure 5 .
Figure 5. (a) A sketch illustrating the introduction of interface coupling frustrations between FM and AFM layers.Ferromagnetic interface coupling is denoted by orange boxes, while antiferromagnetic interface coupling is denoted by grey boxes.(b) Hysteresis loop for FM1/AFM1/FM2/AFM2 system with different interface coupling frustration P int2 at AFM1/FM2 interface.Ms represents the saturation magnetization of the FM layers.(c) Illustration of the b eff dependence on the P int2 .The inset shows the definition of b eff .